Our aim in this article is to study the long time behavior of a class of reaction-diffusion equations in the whole space for which the nonlinearity depends explicitly on the
gradient of the unknown function. We prove the existence of the global attractor and of
exponential attractors for the semigroup associated with the equation. We also consider the
nonautonomous case, and when the forcing term depends quasiperiodically on the time, we
prove the existence of uniform and uniform exponential attractors.